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E-raamat: Game-Theoretical Models in Biology

(Virginia Commonwealth University, USA), (City, University of London, UK)
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Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology, Second Edition presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In addition, the authors explore many applications of game theory to biology, making the text useful to biologists as well.

The book describes a wide range of topics in evolutionary games, including matrix games, replicator dynamics, the hawk-dove game, and the prisoner’s dilemma. It covers the evolutionarily stable strategy, a key concept in biological games, and offers in-depth details of the mathematical models. Most chapters illustrate how to use Python to solve various games.

Important biological phenomena, such as the sex ratio of so many species being close to a half, the evolution of cooperative behaviour, and the existence of adornments (for example, the peacock’s tail), have been explained using ideas underpinned by game theoretical modelling. Suitable for readers studying and working at the interface of mathematics and the life sciences, this book shows how evolutionary game theory is used in the modelling of these diverse biological phenomena.

In this thoroughly revised new edition, the authors have added three new chapters on the evolution of structured populations, biological signalling games, and a topical new chapter on evolutionary models of cancer. There are also new sections on games with time constraints that convert simple games to potentially complex nonlinear ones; new models on extortion strategies for the Iterated Prisoner’s Dilemma and on social dilemmas; and on evolutionary models of vaccination, a timely section given the current Covid pandemic.

Features

  • Presents a wide range of biological applications of game theory.
  • Suitable for researchers and professionals in mathematical biology and the life sciences, and as a text for postgraduate courses in mathematical biology.
    • Provides numerous examples, exercises, and Python code.


  • Covering the major topics of evolutionary game theory, this book presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. The text is also useful to biologists.

    Arvustused

    "It is hard to imagine that the book by Broom & Rychtar is already a decade old, it stills feels fresh! However, in a second edition, the authors have now successfully addressed several novel topics that have developed rapidly in these past 10 years, such as the evolution of cancer or vaccination games. On top of the excellent structure of the original edition of this book, including great exercises, the authors have now included python code and pointers to relevant packages. This is an excellent way to make a new generation of game theorists familiar with the field and at the same time allow them a much more interactive experience!

    The new edition of this wonderful book proves that evolutionary game theory is alive and kicking!" Arne Traulsen, Director, Max Planck Institute for Evolutionary Biology, Germany

    "The second edition of Game-Theoretical Models in Biology shows the tremendous development and applications that this theory has undergone since its inception fifty years ago. That fact that this theory is still undergoing development and finding new applications is evidenced by the fact that the authors have included completely new chapters reflecting, for example, recent applications in the study of cancer evolution or evolution on graphs in the second edition. The book is suitable both for students of mathematical disciplines, to whom it will show the strong application of mathematics in biology, and for students of biological disciplines, who want to gain a solid theoretical basis for the description of eco-evolutionary laws. It is the most comprehensive treatise on the applications of evolutionary game theory in evolutionary and population biology. " Vlastimil Kivan, University of South Bohemia, Czech Republic

    "If you want a solid foundation in the topic of game theory in biology, then work your way through this book. It is an authoritative account of the basics, introduces many important biological applications, and has a plethora of insights. Really excellent." John McNamara, Emeritus Professor at University of Bristol, United Kingdom "In this update of their 2013 book, Broom and Rychtar continue to provide a valuable resource to any researcher interested in evolutionary games. Readers of the original book will especially appreciate the new chapters/sections on recent developments and applications in the field as well as the expanded bibliography. The book will also serve as an excellent self-contained text, with an extensive set of exercises in each chapter, for students at a graduate or senior undergraduate level studying game-theoretic applications to biology" Ross Cressman, Wilfrid Laurier University, Canada

    1. Introduction. 1.1. The History of Evolutionary Games. 1.2. The Key
    Mathematical Developments. 1.3. The Range of Applications. 1.4. Reading this
    Book.
    2. What is a Game? 2.1. Key Game Elements. 2.2. Games in Biological
    Settings. 2.3. Further Reading. 2.4. Exercises.
    3. Two Approaches to Game
    Analysis. 3.1. The Dynamical Approach. 3.2. The Static Approach ESS. 3.3.
    Dynamics Versus Statics. 3.4. Python Code. 3.5 Further Reading. 3.6
    Exercises.
    4. Some Classical Games. 4.1. The Hawk-Dove Game. 4.2. The
    Prisoners Dilemma. 4.3. The War of Attrition. 4.4. The Sex Ratio Game. 4.5.
    Python Code. 4.6. Further Reading. 4.7. Exercises.
    5. The Underlying Biology.
    5.1. Darwin and Natural Selection. 5.2. Genetics. 5.3. Games Involving
    Genetics. 5.4. Fitness, Strategies and Players. 5.5. Selfish Genes: How can
    Non-Beneficial Genes Propagate? 5.6. The Role of Simple Mathematical Models.
    5.7. Python Code. 5.8. Further Reading. 5.9. Exercises.
    6. Matrix Games. 6.1
    Properties of ESSs. 6.2. ESSs in a 2 × 2 Matrix Game. 6.3. Haighs Procedure
    to Locate all ESSs. 6.4. ESSs in a 3 × 3 Matrix Game. 6.5. Patterns of ESSs
    6.6. Extensions to the Hawk-Dove Game. 6.7. Python Code. 6.8. Further
    Reading. 6.9. Exercises.
    7. Nonlinear Games. 7.1 Overview and General Theory.
    7.2. Linearity in the Focal Player Strategy and Playing the Field. 7.3.
    Nonlinearity Due to Non-Constant Interaction Rates. 7.4. Nonlinearity due to
    Games with Time Constraints. 7.5. Nonlinearity in the Strategy of the Focal
    Player. 7.6. Linear Versus Nonlinear Theory. 7.7. Python Code. 7.8. Further
    Reading. 7.9. Exercises.
    8. Asymmetric Games. 8.1. Seltens Theorem for Games
    with Two Roles. 8.2. Bimatrix Games. 8.3. Uncorrelated AsymmetryThe
    Owner-Intruder Game. 8.4. Correlated Asymmetry. 8.7. Python Code. 8.8.
    Further Reading. 8.9. Exercises.
    9. Multi-player Games. 9.1. Multi-player
    Matrix Games. 9.2. The multi-player War of Attrition. 9.3 Structures of
    Dependent Pairwise Games. 9.7. Python Code. 9.8. Further Reading. 9.9.
    Exercises.
    10. Extensive Form Games and other Concepts in Game Theory. 10.1.
    Games in Extensive Form. 10.2. Perfect, imperfect and incomplete information.
    10.3. Repeated games. 10.4. Python Code. 10.5. Further Reading. 10.6.
    Exercises.
    11. State-based Games. 11.1. State-based Games. 11.2. A Question
    of Size. 11.3. Life History Theory. 11.7. Python Code. 11.8. Further Reading.
    11.9. Exercises.
    12. Games in Finite Populations and on Graphs. 12.1. Finite
    Populations and Stochastic Games. 12.2. Games in Finite Populations. 12.3.
    Evolution on Graphs. 12.4 Games on Graphs. 12.7. Python Code. 12.8. Further
    Reading. 12.9. Exercises.
    13. Evolution in Structured Populations. 13.1.
    Spatial Games and Cellular Automata. 13.2. Theoretical Developments for
    Modelling General Structures. 13.3. Evolution in Structured Populations with
    Multi-Player Interactions. 13.4. More Multi-Player Games. 13.5. Evolving
    Population Structures. 13.7. Python Code. 13.8. Further Reading. 13.9.
    Exercises.
    14. Adaptive Dynamics. 14.1. Introduction and Philosophy. 14.2.
    Fitness Functions and the Fitness Landscape. 14.3. Pairwise Invasibility and
    Evolutionarily Singular Strategies. 14.4. Adaptive Dynamics with Multiple
    Traits. 14.5. The Assumptions of Adaptive Dynamics. 14.6. Python Code. 14.7.
    Further Reading. 14.8. Exercises.
    15. The Evolution of Cooperation. 15.1. Kin
    Selection and Inclusive Fitness. 15.2. Greenbeard Genes. 15.3. Direct
    Reciprocity: Developments of the Prisoners Dilemma. 15.4. Public Goods
    Games. 15.5. Indirect Reciprocity and Reputation Dynamics. 15.6. The
    Evolution of Cooperation on Graphs. 15.7. Multi-level Selection. 15.8. Python
    Code. 15.9. Further Reading. 15.10. Exercises.
    16. Group Living. 16.1. The
    Costs and Benefits of Group Living. 16.2. Dominance Hierarchies: Formation
    and Maintenance. 16.3. The Enemy without: Responses to Predators. 16.4. The
    Enemy Within: Infanticide and Other anti-social Behaviour. 16.5. Python Code.
    16.6. Further Reading. 16.7. Exercises.
    17. Mating Games. 17.1. Introduction
    and Overview. 17.2. Direct Conflict. 17.3. Indirect Conflict and Sperm
    Competition. 17.4. The Battle of the Sexes. 17.5. Python Code. 17.6. Further
    Reading. 17.7. Exercises.
    18. Signalling Games. 18.1. The Theory of
    Signalling Games. 18.2. Selecting Mates: Signalling and the Handicap
    Principle. 18.3. Alternative Models of Costly Honest Signalling. 18.4.
    Signalling without Cost. 18.5. Pollinator Signalling Games. 18.6. Python
    Code. 18.7. Further Reading. 18.8. Exercises.
    19. Food Competition. 19.1.
    Introduction. 19.2. Ideal Free Distribution for a Single Species. 19.3. Ideal
    Free Distribution for Multiple Species. 19.4. Distributions at and Deviations
    from the Ideal Free Distribution. 19.5. Compartmental Models of
    kleptoparasitism. 19.6. Compartmental Models of Interference. 19.7.
    Producer-scrounger Models. 19.8. Python Code. 19.9. Further Reading. 19.10.
    Exercises.
    20. Predator-prey and host-Parasite Interactions. 20.1.
    Game-theoretical Predator-prey Models. 20.2. The Evolution of Defence and
    Signalling. 20.3. Brood Parasitism. 20.4. Parasitic Wasps and the Asymmetric
    war of Attrition. 20.5. Complex Parasite Lifecycles. 20.6. Search Games
    Involving Predators and Prey. 20.7. Python Code. 20.8. Further Reading. 20.9.
    Exercises.
    21. Epidemic models. 21.1. SIS and SIR models. 21.2. The Evolution
    of virulence. 21.3. Viruses and the Prisoners Dilemma. 21.4. Vaccination
    models. 21.5. Python Code. 21.6. Further Reading. 21.7. Exercises.
    22.
    Evolutionary Cancer Modelling. 22.1. Modelling Tumour Growth an Ecological
    Approach to Cancer. 22.2. A Spatial Model of Cancer Evolution. 22.3. Cancer
    therapy as a game-theoretic Scenario. 22.4. Adaptive Therapies. 22.5. Python
    Code. 22.6. Further Reading. 22.7. Exercises.
    23. Conclusions. 23.1. Types of
    Evolutionary Games used in Biology. 23.2. What Makes a Good Mathematical
    Model? 23.3. Future Developments. A. Python.
    Mark Broom is a professor of mathematics at City, University of London. For over 30 years, he has carried out mathematical research in game theory applied to biology. His major research themes include multi-player games, patterns of evolutionarily stable strategies, models of parasitic behavior (especially kleptoparasitism), the evolution of defence and signalling, and evolutionary processes in structured populations. He earned his PhD in mathematics from the University of Sheffield.







    Jan Rychtá

    is a professor of mathematics at Virginia Commonwealth University. Prior to joining VCU, he was a Professor at UNC Greensboro. He works on game theoretical models and mathematical models of kleptoparasitism. His recent research interests include mathematical biology and game theory. He earned his PhD in mathematics from the University of Alberta.